Corey Lionis
The University of Melbourne
Corey Lionis is unmarried and has no children, but is one of seven siblings across four parents. They have travelled a bit in Europe and to New Zealand, though nowhere near as much as they would like to. They know fragments of several languages, but speak none of them confidently, and are a novice at bouldering. They are a proficient musician, playing violin, piano, and guitar. Regrettably, they have no experience with the shakuhachi.
Corey is studying algebraic geometry and is interested in everything pure mathematics. They are also generally enthusiastic about physics, computer science, and mathematics more broadly.
Can you give me a quick rundown about the type of mathematics you are studying and its potential impacts for the broader community (think how you would explain your work and studies to others who don’t study maths)
Broadly I study algebraic geometry, and I have just begun specialising to the affine Grassmannian and more generally moduli spaces. The classical Grassmannian is a geometric space with points which classify linear subspaces of a space. The affine Grassmannian is an algebraic version of this, which classifies lattices inside a more generalised object (lattices look like grids of points). In my research I am hoping to understand this space geometrically – how do the points fit together? What kinds of subspaces are in the space? Answering these and related questions has consequences for mathematical physics and the geometric Langlands program.
How did you get into mathematics/statistics/data science? Was there someone or something that inspired you to this field?
I was very fortunate to have meetings with a lot of fantastic, passionate maths people throughout my high-school education, though I didn’t realise I wanted to do maths until later. In my first year of VCE, I was really inspired by my teacher Sharon Long, who had a lot of passion for the abstract problem-solving aspect of mathematics which I hadn’t really been exposed to before. In year 12, Burkard Polster gave a public talk at La Trobe university in Bendigo that I attended, which gave me my first taste of pure mathematics at a university level. My lecturer Santiago Barrera Acevedo imparted to me a strong sense of the lovely ways that geometry, analysis, and algebra come together in higher maths through bonus lectures for my Multivariable Calculus class, which got me completely hooked. Looking back there’s a clear trajectory, but until taking that class I was very firmly convinced that I wanted to study physics or computer science.
You received a Travel Grant to attend AMSI Summer School 2025. How important was this in terms of your ability to attend, fully participate in the program and meet others studying in similar fields? Do you think it was an advantage to attend the program in-person?
The AMSI travel grant enabled me to attend the program in person, which was an invaluable opportunity. I was able to engage deeply with the class and get lots of problem practice because I was studying around other passionate people, and could chat with Zsuzsanna, Damien, and Nelson in office hours for things I didn’t understand.
What was the most valuable part of the program for you?
The most valuable part of the program was definitely the friends and connections I made by being there! I really felt welcome in the AMSI community and made a lot of progress on building a good mathematical mentality.
In the long-term, what do you think are the benefits of having attended Summer School?
I think I strengthened a lot of soft skills which are helpful for working in a maths-related field, including my self-confidence and strategies for effectively approaching hard problems and interpersonal skills for collaborative work.
Summer School included a special Careers Day program which aims to help give students an idea of the kinds of career paths available to maths graduates in industry and private sector research areas. Do you feel better equipped to explore career options in the mathematical sciences after attending AMSI Summer School?
It was great to see that so many industry professionals value the education and training of maths students – before attending, I was under the impression that the skills we’re developing throughout study were only considered valuable if a job candidate could communicate well the broader benefits they had gained from higher academic study.
What advice would you give to someone who is considering applying for Summer School in 2026? Should they apply and why?
I would emphatically recommend attending! If they’re already really interested in mathematics, AMSI will expose them to new ideas, help them improve their academic and collaborative skills, and give them the chance to make new connections with young mathematicians across Australia! If they’re peripherally interested in mathematics, attending AMSI will give them a good taste of further study in mathematics, and give them knowledge and skills they can apply in their broader studies.
What are your current career ambitions in the mathematical sciences sector?
I’d like to continue to a PhD in a related area to my current research. I’m also thinking about other options, primarily programming/software development or secondary school teaching.
How did connecting with the community at AMSI Summer School support your experience?
I really benefited from the diversity of personalities at AMSI – learning about others’ interests, goals, and perspectives on mathematics helped me feel a part of the community and gave me a richer course experience. It was especially helpful hearing the perspectives of people at different levels of study, and those of people who had worked in industry or were planning to.
Any other feedback/comments you would like to provide on the AMSI Travel Grant or AMSI Summer School 2025?
I’d like to thank the AMSI coordinators again for bringing this program together, my tutors and lecturer for their support throughout the unit, and my friends and peers for making AMSI so much fun! Also a huge thank you to AMSI for providing me with the opportunity to take this course in person – learning Algebraic Knot Theory in Sydney was a fantastic way to start 2025!